Know when edit-mode is entered by script? (python)
In your modal operator you can test object.mode for which mode the object is in - example:

import bpy

bpy.context.active_object.mode   # = 'OBJECT'

bpy.ops.object.mode_set(mode='EDIT')

bpy.context.active_object.mode   # = 'EDIT'


There is no callback, you will need to test this on 'tab' event or always to be sure..